How to make voronoi move like living ants?
I don't think the Blender Voronoi has access to quite the same parameter as the one illustrated. Typical shader-Voronoi is based on the distances between randomly placed points, one to a cell, in a regular grid of rectangular cells. I think the specific 'wobble' effect you show is based on smoothly varying the positions of those points within the cells, without moving the cells. 

Close enough, for this effect, might be to use the frame number to drive the Z component of 3D Voronoi, pushing the texture through our 2D XY slice. (The 'Flicker' path in the tree below.)

To drive a value in a shader node by frame number, just type #frame into the relevant field.

Having started, I couldn't resist following the rest of the instructions in your link:



With this sort of result:



I don't think it would be impossible to roll-your-own Voronoi, to give access to the noise generating the per-cell points.. or maybe there's a better way.